Non-autonomous interacting particle systems in continuum

Abstract

A conservative Feller evolution on continuous bounded functions is constructed from a weakly continuous, time-inhomogeneous transition function describing a pure jump process on a locally compact Polish space. The transition function is assumed to satisfy a Foster-Lyapunov type condition. The results are applied to interacting particle systems in continuum, in particular to general birth-and-death processes (including jumps). Particular examples such as the BDLP and Dieckmann-Law model are considered in the end.

Published in Methods of Functional Analysis and Topology (MFAT), available at http://mfat.imath.kiev.ua/article/?id=891

References in corpus (2)

• A microscopic probabilistic description of a locally regulated population and macroscopic approximations
• Spatial birth and death processes as solutions of stochastic equations

Cited by in corpus (3)

• Non-equilibrium dynamics for a Widom-Rowlinson type model with mutations
• Stochastic averaging for a spatial population model in random environment
• Weak-coupling limit for ergodic environments